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This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

Two-dimensional incompressible fluid flows around a rectangular shape placed over a larger rectangular shape at low Reynolds numbers (Re) have been numerically analyzed in the present work. The vortex shedding is investigated at different arrangements of the two shapes allowing the investigation of three possible configurations. The calculations are carried out for several values of Re ranging from 1 to 200. The effect of the obstacle geometry on the vortex shedding is analyzed for crawling, steady and unsteady regimes. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. This paper aims to observe that the transition of the unsteady regime is performed by a Hopf bifurcation. The critical Re beyond which the flow becomes unsteady is determined for each configuration. A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best configuration in terms of both drag and lift. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Re and the obstacle geometry. Hence, the values of vortex shedding frequencies are calculated in this work.

The dimensionless Navier–Stokes equations were numerically solved using the following numerical technique based on the finite volume method. The temporal discretization of the time derivative is performed by an Euler backward second-order implicit scheme. Non-linear terms are evaluated explicitly; while, viscous terms are treated implicitly. The strong velocity–pressure coupling present in the continuity and the momentum equations are handled by implementing the projection method.

The present paper aims to numerically study the effect of the obstacle geometry on the vortex shedding and on the drag and lift forces to analyze the flow structure around three configurations at crawling, steady and unsteady regimes.

A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best shapes configuration in terms of both drag and lift.

This paper aims to study the fluid flow and forced convection heat transfer from an isothermal circular cylinder with control rods in the laminar unsteady flow regime.

The overset grid method was used for accurate simulation of the unsteady flows around different arrangements of the cylinders. Grid generation for overset grids was performed using a general orthogonal boundary fitted coordinate system. The method of solution was based on a finite volume discretization of the Navier-Stokes equations. Simulations were carried out for the Prandtl numbers of 0.7 and 7.0 with the Reynolds numbers ranging from 60 to 300.

The results indicate that the performance of multiple control rods depends strongly on the spacing ratio. Furthermore, in a manner similar to the flow patterns, four different thermal regimes were recognized based on the variations of mean Nusselt number versus G/D, as the thermal regimes follow the categories of flow regimes at different diameter ratios. However, for different Prandtl numbers, no single trend of heat transfer variation versus the spacing ratio exists for same regime.

Few studies have been conducted to investigate the heat transfer characteristics from control rods. The results of this study provide a comprehensive knowledge on the dynamical and thermal behavior of the flow around multiple cylinders.

A three‐dimensional numerical investigation of flow field and heat transfer in sine‐wave crossed ducts is presented. Numerical simulations are carried out using a finite element procedure based on an algorithm which shares many features with the SIMPLER finite‐volume method, and utilizes equal order pressure–velocity interpolation functions. Since the flow, after a short entrance regime, reaches the fully developed condition, the computational domain can be reduced to a single periodic element and periodic boundary conditions are assumed at the entrance, the exit and the sides. The thermal performance and the frictional pressure losses of the crossed‐corrugated plates are investigated for different Reynolds number, from steady up to transitional regimes. The evolution from steady to unsteady flow structure is detected and the influence of the unsteadiness on heat transfer and on pressure drop is analysed. Simulations are performed for both air (Pr=0.7) and water (Pr=7) as the flow medium and the dependence of Nusselt number on Prandtl number is investigated.

The purpose of this paper is to study the effects of Angle of Attack (AOA), Axis Ratio (AR) and Reynolds number (Re) on unsteady laminar flow over a stationary elliptic cylinder.

The governing equations of fluid flow over the elliptic cylinder are solved numerically on a Cartesian grid using Projection method based Immersed Boundary technique. This numerical method is validated with the results available in open literature. This scheme eliminates the requirement of generating a new computational mesh upon varying any geometrical parameter such as AR or AOA, and thus reduces the computational time and cost.

Different vortex shedding patterns behind the elliptic cylinder are identified and classified using time averaged centerline streamwise velocity profile, instantaneous vorticity contours and instantaneous streamline patterns. A parameter space graph is constructed in order to reveal the dependence of AR, AOA and Re on vortex shedding. Integral parameters of flow such as mean drag, mean lift coefficients and Strouhal number are calculated and the effect of AR, AOA and Re on them is studied using various pressure and streamline contours. Functional relationships of each of integral parameters with respect to AR, AOA and Re are proposed with minimum percentage error.

The results obtained can be used to explain the characteristics of flow patterns behind slender to bluff elliptical cylinders which found applications in insect flight modeling, heat exchangers and energy conservation systems. The proposed functional relationships may be very useful for the practicing engineers in those fields.

The results presented in this paper are important for the researchers in the area of bluff body flow. The dependence of AOA on vortex shedding and flow parameters was never reported in the literature. These results are original, new and important.

The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.

The numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.

This model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.

Bearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).

A sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.

The formulation being presented is competitive and could be considered as a potential alternative to other approaches.

The purpose of this paper is to simulate the flow of a conducting fluid past a circular cylinder placed centrally in a channel subjected to an imposed transverse magnetic field to study the effect of a magnetic field on vortex shedding at different Reynolds numbers varying from 50 to 250.

The two‐dimensional incompressible laminar viscous flow equations are solved using a second‐order implicit unstructured collocated grid finite volume method.

An imposed transverse magnetic field markedly reduces the unsteady lift amplitude indicating a reduction in the strength of the shed vortices. It is observed that the periodic vortex shedding at the higher Reynolds numbers can be completely suppressed if a sufficiently strong magnetic field is imposed. The required magnetic field strength to suppress shedding increases with Reynolds number. The simulation shows that the separated zone behind the cylinder in a steady flow is reduced as the magnetic field strength is increased.

In this paper, due attention is given to resolve and study the unsteady cylinder wake and its interaction with the shear‐layer on the channel wall in the presence of a magnetic field. A critical value of the Hartmann number for complete suppression of the shedding at a given Reynolds number is found.

The purpose of this paper is to analyse the convective heat transfer of an unsteady pulsed, laminar, incompressible flow in axisymmetric tubes with periodic sections. The flow is supposed to be developing dynamically and thermally from the duct inlet. The wall is heated at constant and uniform temperature.

The problem is written with classical homogeneous boundary conditions. We use a shift operator to impose non‐homogeneous boundary conditions. Consequently, this method introduces source terms in the Galerkin formulation. The momentum equations and the energy equation which govern this problem are numerically solved in space by a spectral Galerkin method especially oriented to this situation. A Crank‐Nicolson scheme permits the resolution in time.

From the temperature field, the heat transfer phenomenon is presented, discussed and compared to those obtained in straight cylindrical pipes. This study showed the existence of zones of dead fluid that locally have a negative influence on heat transfer. Substantial modifications of the thermal convective heat transfer are highlighted at the entry and the minimum duct sections.

Pulsated flows in axisymmetric geometries can be applied to medical industries, mechanical engineering and technological processes.

One of the original features of this study is the choice of Chebyshev polynomials basis in both axial and radial directions for spectral methods, combined with the use of a shift operator to satisfy non‐homogeneous boundary conditions.

This study aims to investigate the wake behind an oscillating airfoil at a various angle of incidence and Reynolds number in a deep dynamic stall condition.

NACA 0012 airfoil is allowed to undergo harmonic pitching motion about the quarter chord axis at Reynolds numbers of 0.5 * 105, 1.17 * 105, 1.7 * 105 and 2.12 * 105, and the reduced frequency of 0.1. The experiments are conducted at a set of mean and amplitude angle of attack that covered the angle of incidence from −5° to 25°. The wake rake is placed at a distance of one chord from the trailing edge of the airfoil.

The hysteresis of the flow during the upstroke and the downstroke motion are captured. The huge growth in the velocity defect and the wake thickness beyond the angle of attack of 15° explicate the appearance of the strong unsteady effects on the wake. The results also show that at the reduced frequency of 0.1, the wake structure is of drag producing type due to the momentum deficit.

Streamwise velocity profile and the turbulent intensity profiles are presented to show the effects of Reynolds number and angle of incidence on the wake behind the oscillating airfoil at the reduced frequency of 0.1, and in the intermediate range of Reynolds number is the novelty of the study.

This paper aims to analyze the effect of aspect ratio A and aspect velocity ratio a on the bifurcation occurrence phenomena in lid-driven cavity by using finite volume method (FVM) and multigrid acceleration. This study has been performed for certain pertinent parameters; a wide range of the Reynolds number values has been adopted, and aspect ratios ranging from 0.25 to 1 and various velocity ratios from 0.25 to 0.825 have been considered in this investigation. Results show that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity has been verified through time history plots for the velocity component and phase-space trajectories as a function of Reynolds number. Velocity profile for special case of a square cavity (A = 1) was found to be in good agreement between current numerical results and published ones. Flow characteristics inside the cavity have been presented and discussed in terms of streamlines and vorticity contours at a fixed Reynolds number (Re = 5,000) for various aspect ratios (a = 0).

The numerical method is based on the FVM and multigrid acceleration.

Computations have been investigated for several Reynolds numbers and aspect ratios A (0.25, 0.5, 0.75, 0.825 and 1). Besides, various velocity ratios (a = 0.25, 0.5, 0.75 and 0.825) at fixed aspect ratios (A = 0.25, 0.5 and 0.75) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of Hopf bifurcation, giving rise to a perfectly periodic state. Flow periodicity is verified through time history plots for velocity components and phase-space trajectories.

The bifurcations between steady and unsteady states are investigated.